Convoluted $C$-cosine functions and convoluted $C$-semigroups

M. Kostic

Abstract: Convoluted $C$-cosine functions and convoluted $C$-semigroups are introduced and investigated.Then their relations to the well-posedness of second order abstract Cauchy problem and the $\Theta $-convoluted $C$-regularized Cauchy problem are studied. Generation results for convoluted $C$-semigroups are given.